This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A248052 #14 Oct 02 2014 05:40:22 %S A248052 1,2,1,8,7,7,5,1,25,35,15,14,13,12,1,4,23,532,22,385,113,1,17,138,8, %T A248052 92,80,44,116,128,586,165,5,464,10,39,80,38,1,52,33,118,6,28,11,1239, %U A248052 47,92,517,3,145,40,8,184,104,104,16,73,53,52,5,145,172,68,11 %N A248052 Least positive integer m such that m + n divides pi(m^2) + pi(n^2), where pi(x) denotes the number of primes not exceeding x. %C A248052 Conjecture: (i) a(n) exists for any n > 0. %C A248052 (ii) For each integer m > 0, there is a positive integer n such that m + n divides prime(m^2) + prime(n^2). %H A248052 Zhi-Wei Sun, <a href="/A248052/b248052.txt">Table of n, a(n) for n = 1..1000</a> %H A248052 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685, 2014. %e A248052 a(4) = 8 since 8 + 4 = 12 divides pi(8^2) + pi(4^2) = 18 + 6 = 24. %t A248052 Do[m=1;Label[aa];If[Mod[PrimePi[m^2]+PrimePi[n^2],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,70}] %t A248052 a[ n_] := If[ n<1, 0, Module[ {m=1}, While[ Not @ Divisible[ PrimePi[m^2] + PrimePi[n^2], m + n], m++]; m]]; (* _Michael Somos_, Sep 30 2014 *) %Y A248052 Cf. A000040, A000720, A247824, A247975, A248044, A248054. %K A248052 nonn %O A248052 1,2 %A A248052 _Zhi-Wei Sun_, Sep 30 2014